2a^2-6a=a^2-a+6

Solution for 2a^2-6a=a^2-a+6 equation:

2a^2-6a=a^2-a+6

We move all terms to the left:

2a^2-6a-(a^2-a+6)=0

We get rid of parentheses

2a^2-a^2-6a+a-6=0

We add all the numbers together, and all the variables

a^2-5a-6=0

a = 1; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·1·(-6)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*1}=\frac{-2}{2}
=-1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*1}=\frac{12}{2}
=6
$